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Sadducees

Often we in the modern time totally conflate Sadducees and Pharisees but they are as Republicans and Democrats today... very much not the same

Origin

Back in the Davidic kingdom they are the group that sought to restore the priesthood by way of lineage. A goal was figuring out who the High Priest was. Lots are cast and Zaddok is chosen at some point - his line becomes the Jesus-era Saducees. They are the zaddokim (Hebrew pronounciation) which when somwhat anglosized becomes sadducees.

Hasmonean

During Seleucids destruction of the Temple the Maccabeans revolt and expel Selecuis and Ptolemies. The Hasmonean kingdom follows this, which are priests that the Maccabeans turned the kingdom over to in an effort to be 'people of the text'

Hasmoneans are 7 famlies that have descended from Zaddok. Over the course of 2-3 decades they become entirely Hellenistic. These ones are known in the Gospels as the Chief Priests which is a different group than teachers of the Law

The Chief Priests are a corrupt religious Mafia

Originally "Saducee" referred to direct descendents of Zaddok, which are a subset of Levitical descendents. Come Jesus-time Saduccee becomes anyone who agrees with the priestly system... Not all priests were Saducees (See Zachariah - father of John the Baptist. He was a righteous priest which didn't exist in their day - he was not a Saducee, he was faithful to Torah not Hellenism)

Rome's Influence

Herod essentially controlled the world's wealth due to his own position as king (of where?). Hasmonean's persued Herod and asked him to marry a Hasmonean daughter in order to be called Jewish. Hasmoneans did this as they saw their time coming to an end with the rising power of Rome. Herod saw the opportunity, took it, and then he extends an olive branch to Caesar - and Caesar accepts the partnership which turns Herod into basically a puppet king of Judea

Herod then begins to auction off the High Priesthood - furthering priestly corruption. Annas (Caiphas is Annas' son) is the one who buys the priesthood - and the priesthood stays with this family until the destruction of Jerusalem in AD 70.

Timeline